Parallel spin wave for the Villain model (Paul Dario, CY Cergy Paris Université)

24.11.2025 16:15 – 18:00

Abstract:
This talk will focus on the decay of correlations in the Villain model. We consider the low-temperature regime in dimensions d>3, where it is conjectured that the cosine-cosine correlation between two spins decays like the inverse of their distance to the power 2(d-2). The work of Bricmont, Fontaine, Lebowitz, Lieb, and Spencer (1982) shows that this correlation decays at least as fast as the inverse distance to the power d-2. I will present a recent result that improves this bound to an exponent of d-1, up to a logarithmic correction.

The proof builds on a key insight of Fröhlich and Spencer (1982): at low temperature, a duality transformation combined with a renormalisation argument can be used to map the Villain model to a variant of the well-studied \nabla\phi interface model. This latter model can then be analysed precisely using the Helffer–Sjöstrand formula together with elliptic regularity estimates.

Joint work with W. Wu.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-15, Séminaire Math Physics

entrée libre